Guess I'll start with whats new.
Starter, Solenoid, Fuseable Link and associated wires.
Cleaned and dried both fuse boxes,.. yes they were wet.

Still when I turn the key or jump the solenoid the power cable to the starter gets hot enough to nearly melt itself. starter has been bench tested all grounds redone.

 

I am assuming a lot because you're not giving out much info (year, engine, etc) but check and make sure your engine isn't locked up. Try turning it by hand. 5-speed?? Can ya push start it? That's where I would start. Getting the idea your starter is engaging but not able to turn the motor. But you aren't clear about that.